A horizontal force of 150 N is used to push a 32.5-kg packing crate a distance of 4.95 m on a rough horizontal surface. If the crate moves at constant speed, find each of the following.
(a) the work done by the 150-N force?
(b) the coefficient of kinetic friction between the crate and the surface ?
Wc = m*g = 32.5kg * 9.8N/kg = 318.5 N.=
Wt. of crate.
Fc = 318.5N [0o]
Fp = 318.5*sin(0) = 0 = Force parallel to surface.
Fv = 318.5*cos(0) = 318.5 N. = Force perpendicular to surface.
a. Work = F*d = 150 * 4.95 = 742.5 Joules.
b. Fap-u*Fv = m*a
150-Fp-u*Fv = m*a
150-0-318.5u = m*a = m*0 = 0
318.5u = 150
u = 0.470.
(a) To find the work done by the 150-N force, we need to use the equation for work:
Work = Force x Distance x cos(theta)
Where:
- Work is the amount of energy transferred to an object by a force,
- Force is the magnitude of the applied force,
- Distance is the distance the object moves in the direction of the force,
- Theta is the angle between the applied force and the direction of motion.
In this case, the crate moves in the same direction as the applied force, so the angle theta is 0 degrees. Therefore, the equation simplifies to:
Work = Force x Distance
Substituting the given values:
Force = 150 N
Distance = 4.95 m
Work = 150 N x 4.95 m = 742.5 J
Therefore, the work done by the 150-N force is 742.5 Joules.
(b) To find the coefficient of kinetic friction between the crate and the surface, we need to use the following equation:
Frictional force = coefficient of kinetic friction x Normal force
Where:
- Frictional force is the resisting force acting on the crate due to the rough surface,
- Coefficient of kinetic friction is a dimensionless quantity that represents the roughness between two surfaces in contact,
- Normal force is the perpendicular force exerted on the crate by the surface.
Since the crate is moving at a constant speed, we know that the net force acting on the crate is zero. Therefore, the frictional force must be equal in magnitude but opposite in direction to the applied force.
Thus, we have:
Frictional force = Applied force = 150 N
To find the normal force, we need to use Newton's second law:
Sum of forces = mass x acceleration
Since the crate is moving at constant speed, the acceleration is zero. Therefore, the sum of forces acting on the crate must be zero as well.
Sum of forces = Applied force - Frictional force - Normal force = 0
Rearranging the equation, we get:
Normal force = Applied force - Frictional force
Substituting the given values:
Applied force = 150 N
Frictional force = 150 N
Normal force = 150 N - 150 N = 0 N
Since the normal force is zero, it means that there is no vertical force acting on the crate. This suggests that the crate is on a horizontal surface.
Therefore, the coefficient of kinetic friction between the crate and the surface is zero.
Note: In physics, the coefficient of friction can range from 0 (no friction) to 1 (maximum friction).