A grocery cart with a mass of 18 kg is pushed at constant speed along an aisle by a force F = 12 N. The applied force acts at a 20° angle to the horizontal. Find the work done by each of the forces on the cart if the aisle is 14 m long.

work done by the applied force

work done by the frictional force

work done by the normal force

work done by the gravitational force

Thankyou

The applied force is W = Fdcos(theta).

the normal force and gravitaional force do no work, because there is no motion on the y axis

To find the work done by each force, we can use the formula: Work = Force × Distance × cos(θ), where θ is the angle between the force and the direction of motion.

1. Work done by the applied force:
Given: F = 12 N, Distance = 14 m, θ = 20°
Work = 12 N × 14 m × cos(20°)

2. Work done by the frictional force:
The frictional force opposes the motion and acts in the opposite direction of the applied force. Since the cart is moving at constant speed, the net force is zero. Therefore, the frictional force magnitude is equal to the applied force's magnitude.
Given: F = 12 N, Distance = 14 m, θ = 180° (opposite direction)
Work = -12 N × 14 m × cos(180°)

3. Work done by the normal force:
The normal force is perpendicular to the direction of motion. As a result, the angle between the normal force and the displacement is 90°, and cos(90°) = 0. Therefore, the work done by the normal force is zero.

4. Work done by the gravitational force:
The gravitational force acts vertically downward, while the displacement is in the horizontal direction. Therefore, the angle between the gravitational force and the displacement is 90°, and cos(90°) = 0. Hence, the work done by the gravitational force is zero.

To get the numerical values, you'll need to plug the values into the respective equations and calculate the results.

To find the work done by each of the forces on the grocery cart, we need to understand the concept of work. Work is defined as the product of force and the displacement it causes in the direction of the force. Mathematically, work (W) can be calculated using the formula:

W = F * d * cos(θ)

where F is the magnitude of the force, d is the displacement, and θ is the angle between the force vector and the displacement vector.

1. Work done by the applied force:
Given that the applied force (F) is 12 N and it acts at a 20° angle to the horizontal, we can use the formula mentioned above to calculate the work done. The displacement (d) is given as 14 m.
W_applied = F * d * cos(θ)
= 12 N * 14 m * cos(20°)
≈ 227.85 J

So, the work done by the applied force on the cart is approximately 227.85 Joules.

2. Work done by the frictional force:
The work done by the frictional force can be calculated by multiplying the force of friction (which is opposite in direction to the applied force) by the displacement. Since the cart is moving at a constant speed, the net force on it is zero, meaning the force of friction cancels out the applied force. Therefore, the work done by the frictional force is zero.

W_friction = 0 J

3. Work done by the normal force:
The normal force is a perpendicular force exerted by the surface on the cart. Since the displacement is along the horizontal direction and the normal force is perpendicular to it, the angle (θ) between them is 90°. Hence, the cos(θ) term becomes 0, indicating no work is done by the normal force.

W_normal = 0 J

4. Work done by the gravitational force:
The gravitational force acts vertically downward and is given by the weight of the cart, which can be calculated as the mass (m) multiplied by acceleration due to gravity (g). Assuming g to be 9.8 m/s² and the mass (m) of the cart to be 18 kg, the force of gravity (F_gravity) can be found as:
F_gravity = m * g
= 18 kg * 9.8 m/s²
= 176.4 N

Since the displacement is along the horizontal direction and the gravitational force is acting vertically, the angle (θ) between them is 90°. Therefore, the cos(θ) term becomes 0, indicating no work is done by the gravitational force.

W_gravity = 0 J

To sum up:

Work done by the applied force = approximately 227.85 J
Work done by the frictional force = 0 J
Work done by the normal force = 0 J
Work done by the gravitational force = 0 J