Work Done by Variable Force Apparatus | FrixoDynamics FX-517
The SCIENTICO Work Done by Variable Force Apparatus is a bench-top experimental unit designed to give students a practical, measurable demonstration of the concept that mechanical work done by a variable force equals the area under the force-distance graph. Made by Scientico India, ISO 9001:2015 certified, and supplied with a calibration certificate and operation manual.
The SCIENTICO FrixoDynamics FX-517 Work Done by Variable Force Apparatus is a bench-top experimental unit designed to give students a practical, measurable demonstration of the concept that mechanical work done by a variable force equals the area under the force-distance graph. The apparatus supports two distinct experiment modes, a vertical force mode using a suspended trolley and pulley system, and a tangential force mode using a pivoted arm restrained by a spring balance, each producing a nonlinear force-distance relationship that must be integrated graphically to determine the work done. A 0–100 N spring balance, integrated protractor scale, and ball bearing-mounted pulleys are included as standard. Manufactured by SCIENTICO, the FX-517 is suitable for supply to engineering institutions and distributors worldwide.
Product Overview
Work done by a constant force is straightforwardly calculated as the product of force and displacement. However, when the force varies with position, as is common in real mechanical systems, the work done must be determined by integrating the force over the displacement, which is geometrically equivalent to finding the area under the force-distance curve. The FX-517 demonstrates this principle through two physically distinct experiment configurations that each exhibit clear, measurable nonlinearity.
In the vertical force experiment, a suspension cord carries a loaded trolley at its midspan. The cord passes over a ball bearing-mounted pulley at one end and down to a weight hanger. As the vertical effort load is increased incrementally, the cord moves to a new equilibrium position, lifting the trolley. The height of both the effort hanger and the trolley load are recorded at each increment relative to the base. The resulting effort-versus-displacement graph is nonlinear, and the area under it, determined graphically or numerically, gives the work done in lifting the trolley. This is compared against the change in potential energy of the trolley, providing a direct energy balance verification.
In the tangential force experiment, a pivoted arm carries a load hanger at its free end. A spring balance is attached perpendicular to the arm and restrains it at a defined angular position indicated by the protractor scale on the backboard. The force in the spring balance represents the effort required to hold the weighted arm at that angle. By repeating the measurement at a series of angular positions, and for different applied weights, students obtain a force-versus-angle dataset from which a force-distance curve is constructed. The area under this curve gives the work done in moving the arm through the angular range.
Both experiment modes clearly establish that the force is not constant and that simple force-times-distance multiplication would give an incorrect result, reinforcing why graphical integration is the correct approach for variable force systems.
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model-specific, ISO 9001:2015 compliant. Supplied to universities and institutions in 30+ countries.
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| Parameter | Specification |
|---|---|
| Model | FrixoDynamics FX-517 |
| Experiment Modes | Vertical force (trolley and pulley), Tangential force (pivoted arm) |
| Spring Balance Range | 0 – 100 N |
| Spring Balance Graduation | 0.5 N |
| Angle Measurement | Integrated protractor scale on backboard |
| Pulleys | 3 pulleys, ball bearing-mounted |
| Weight Set | 2 x 0.5 N hangers, 4 x 1 N, 4 x 2 N, 4 x 5 N |
| Hangers | 2 |
| Mounting | Bench-top, support board with backboard |
| Scope of Delivery | 1 experimental unit, 1 spring balance, 2 sets of weights, 2 hangers, 3 pulleys, 1 thread |
Key Features
- Two independent experiment modes, vertical force and tangential force, covering different physical contexts for work done by a variable force
- Spring balance (0–100 N, 0.5 N graduation) provides direct force readings in both experiment modes
- Integrated protractor scale on backboard enables direct angular position reading in the tangential force experiment
- Ball bearing-mounted pulleys minimise friction in the vertical force experiment for accurate effort-displacement data
- Nonlinear force-distance characteristics in both modes make graphical area integration a necessary and clearly demonstrable step
- Work done result directly comparable against change in potential energy for energy balance verification
- Compact bench-top unit with support board and backboard, self-contained, no wall mounting required
- Suitable for both quantitative student experiments and instructor-led demonstrations on mechanical work and energy
Applications
- Experimental determination of the relationship between effort and distance moved in a variable force system
- Demonstration that work done equals the area under a force-distance graph
- Graphical integration of a nonlinear force-distance curve to calculate work done
- Comparison of experimentally determined work done against theoretical change in potential energy
- Investigation of the effect of load magnitude on the effort-displacement relationship in both experiment modes
- Undergraduate laboratory practicals in mechanics, dynamics, energy methods, and applied physics
- Supplementary demonstrations for courses covering potential energy, mechanical advantage, and work-energy principles
Construction and System Design
The FX-517 is mounted on a rigid support board with a vertical backboard that carries the protractor scale for the tangential force experiment. The backboard also provides the fixed mounting point for the pivoted arm. The arm rotates freely about its pivot and carries a load hanger at its free end. The spring balance is attached at right angles to the arm at a defined point, providing a perpendicular restraining force that is read directly from the scale. The angular position of the arm is read from the protractor at the pivot.
For the vertical force experiment, the cord is threaded through the three ball bearing-mounted pulleys. One pulley is fixed at the upper end of the board, redirecting the cord from the horizontal midspan to the vertical effort hanger. The trolley sits on the cord at midspan and is lifted as the cord geometry changes with increasing effort load. Heights of both the trolley and the effort hanger are measured from the base at each load increment, providing the displacement data needed for the force-distance graph.
The spring balance, with its 0.5 N graduation over a 0–100 N range, provides sufficient resolution and capacity for both experiment modes. The weight set, covering 0.5 N to 5 N denominations, allows the applied load to be built up incrementally in either mode, generating enough data points for a well-defined force-distance curve. Thread is included for cord setup in the vertical force experiment.
Export and Supply Capability
The SCIENTICO FrixoDynamics FX-517 is available for supply to engineering colleges, technical universities, mechanical engineering and physics departments, research institutions, and industrial training centres. SCIENTICO manufactures and exports laboratory equipment to institutions and distributors across multiple regions. Standard packaging is suitable for international shipment. Bulk orders, customised configurations, and institutional procurement enquiries are welcomed. Please contact SCIENTICO directly for pricing, lead times, and shipping terms.
Q1: What does the work done by variable force apparatus demonstrate?
The FX-517 demonstrates that when a force varies with displacement, the work done cannot be calculated simply as force multiplied by distance. Instead, it must be determined by finding the area under the force-distance graph, the graphical equivalent of integrating the variable force over the displacement. Both experiment modes on the FX-517 produce clearly nonlinear force-distance relationships, making this distinction physically evident and measurable.
Q2: What are the two experiment modes available on the FX-517?
The first mode is the vertical force experiment, in which a loaded trolley is lifted by a cord routed over ball bearing pulleys. As the effort load is increased incrementally, the cord moves to a new equilibrium position, and the heights of both the trolley and the effort hanger are recorded. The second mode is the tangential force experiment, in which a pivoted arm carrying a load hanger is restrained by a spring balance perpendicular to the arm. The spring balance force and the arm’s angular position are recorded at successive angles for different applied loads.
Q3: How is the work done calculated from the experimental data?
In both modes, students record the restraining force at a series of displacement or angular positions, constructing a force-versus-displacement curve. The area under this curve, determined graphically by counting grid squares or by numerical integration, gives the total work done over the measured range. In the vertical force experiment, this result is compared against the calculated change in potential energy of the trolley, providing an energy balance check.
Q4: Why are ball bearing-mounted pulleys used in the FX-517?
Ball bearing pulleys minimise friction at the cord deflection points in the vertical force experiment. Friction in the pulleys would add an uncontrolled resistance to the cord system, causing the measured effort to exceed the true force required to lift the trolley. By using ball bearing-mounted pulleys, the friction contribution is kept negligibly small, ensuring that the recorded effort-displacement data accurately reflects the force-distance relationship of the trolley lifting mechanism.
Q5: What is included in the scope of delivery for the FX-517?
The FX-517 is supplied as a complete experimental kit including: one work done experimental unit with support board, pivoted arm, protractor backboard, and cord system; one spring balance (0–100 N, 0.5 N graduation); two sets of weights (2 x 0.5 N hangers, 4 x 1 N, 4 x 2 N, 4 x 5 N); two weight hangers; three ball bearing-mounted pulleys; and one thread for cord setup.
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