A force of 1.50 N acts on a 0.200-kg cart so as to accelerate it along an air track. The track and force are horizontal in line. The cart traveled from rest through 30.0 cm. (a) What is the distance traveled in meters? (2 pts) (b) What formula is to be used to calculate the work done by the force on the cart? (1 pt) (c) How much work is done by the force on the cart?
To answer these questions, we will need to apply the formulas and concepts related to work, force, and displacement. Let's go step by step:
(a) What is the distance traveled in meters? (2 pts)
To convert the given distance of 30.0 cm to meters, we need to divide it by 100 because there are 100 centimeters in 1 meter.
So, the distance traveled in meters is 30.0 cm / 100 = 0.30 meters.
(b) What formula is to be used to calculate the work done by the force on the cart? (1 pt)
The formula we can use to calculate work is:
Work (W) = Force (F) * Displacement (d) * cosθ
where:
- W represents the work done by the force (in joules, J),
- F represents the magnitude of the force exerted on the cart (in newtons, N),
- d represents the displacement of the cart in the direction of the force (in meters, m),
- θ represents the angle between the force vector and the displacement vector (if they are not in the same direction).
In this case, the force and displacement are in the same direction, so the angle between them is 0 degrees (cos0 = 1).
Thus, the formula for calculating work in this particular scenario simplifies to:
Work (W) = Force (F) * Displacement (d)
(c) How much work is done by the force on the cart?
We are given that the force acting on the cart is 1.50 N, and the distance traveled by the cart is 0.30 m.
Using the formula for work, we can substitute the values:
Work (W) = 1.50 N * 0.30 m = 0.45 J
Therefore, the work done by the force on the cart is 0.45 joules (J).