how much work is done on a 50kg cart that is pushed 10m at a constant rate of 5m/s^2
To determine the amount of work done on the cart, we can use the formula:
Work = Force × Distance × Cos(θ),
where:
- Force is the amount of force applied to the cart,
- Distance is the distance over which the force is applied, and
- θ is the angle between the force applied and the direction of motion.
In this case, we are given that the cart is pushed at a constant rate of 5 m/s^2, but not explicitly given the force applied. However, we can calculate the force using Newton's second law of motion:
Force = Mass × Acceleration.
Given that the mass of the cart is 50 kg and the acceleration is 5 m/s^2, we can calculate the force:
Force = 50 kg × 5 m/s^2 = 250 N.
Now, we need to determine the direction of the force. Since the cart is being pushed in a straight line, the force will be applied parallel to the direction of motion, which means that θ = 0 degrees.
Substituting the values into the work formula:
Work = 250 N × 10 m × cos(0°).
cos(0°) = 1, as the cosine of 0 degrees is equal to 1.
Work = 250 N × 10 m × 1 = 2500 N·m.
Therefore, the work done on the 50 kg cart that is pushed 10 m at a constant rate of 5 m/s^2 is 2500 joules (J).