A 120 kg crate on the flatbed of a truck that is moving with an acceleration of 1.5 m/s^2 along the positive x axis. The crate does not slip with respect to the truck undergoes a displacement whose magnitude is 43 m. What is the total work done on the crate by all of the forces acting on it?
assignment
To find the total work done on the crate, we need to consider the work done by each force acting on it.
First, let's identify the forces at play:
1. The weight of the crate, which is given by the equation: F_weight = m * g, where m is the mass of the crate and g is the acceleration due to gravity (approximately 9.8 m/s^2).
2. The normal force exerted by the truck bed on the crate. Since the crate does not slip, the normal force is equal in magnitude and opposite in direction to the weight of the crate.
3. The force causing the acceleration of the truck, which is given by the equation: F_acceleration = m * a, where a is the acceleration of the truck.
Now, let's calculate the work done by each force:
1. The work done by the weight of the crate can be calculated using the equation: W_weight = F_weight * d * cos(theta), where d is the displacement and theta is the angle between the direction of the force and the displacement. In this case, since the crate is not moving vertically and the weight is acting vertically downward, the angle theta is 0 degrees. Therefore, the work done by the weight of the crate is zero since the cosine of 0 degrees is 1 and the weight is perpendicular to the displacement.
W_weight = F_weight * d * cos(0) = 0
2. The work done by the normal force is also zero since the normal force is perpendicular to the displacement.
W_normal = F_normal * d * cos(90) = 0
3. The work done by the force causing the acceleration can be calculated as:
W_acceleration = F_acceleration * d * cos(theta)
= (m * a) * d * cos(theta)
= (120 kg * 1.5 m/s^2) * 43 m * cos(0)
= 7722 J
Therefore, the total work done on the crate by all the forces acting on it is:
Total work = W_weight + W_normal + W_acceleration
= 0 + 0 + 7722 J
= 7722 J
Hence, the total work done on the crate is 7722 Joules.