a shopper pushes her 25kg grocery car with a force of 22n inclined at an angle of 60 with horizontal through a distance of 7.50 m. find the work done a) applied force b) friction force answer key
To calculate the work done, we can use the formula:
Work = Force * Distance * cos(theta)
a) Calculating the work done by the applied force:
Given:
Force (applied) = 22 N
Distance = 7.50 m
Theta (angle with horizontal) = 60 degrees
Plugging these values into the formula:
Work (applied force) = 22 N * 7.50 m * cos(60°)
To find the value of cos(60°), we can use the trigonometric identity:
cos(60°) = 0.5
Work (applied force) = 22 N * 7.50 m * 0.5
Now we can calculate the value:
Work (applied force) = 82.5 J
Therefore, the work done by the applied force is 82.5 Joules.
b) Calculating the work done by the friction force:
To calculate the work done by the friction force, we need to know the coefficient of friction between the grocery cart and the surface it's being pushed on. Without this information, it is not possible to determine the work done by the friction force.
To find the work done by a force, we can use the formula:
Work = Force x Distance x cosθ
where:
- Work is the amount of energy transferred or expended by a force,
- Force is the applied force,
- Distance is the distance over which the force is applied,
- θ is the angle between the force and the direction of motion.
a) The work done by the applied force is calculated by substituting the given values into the formula:
Force = 22 N
Distance = 7.50 m
θ = 60°
Work = 22 N x 7.50 m x cos(60°)
To find the cosine of 60 degrees, you can use a calculator or refer to a trigonometric table. The cosine of 60 degrees is 0.5.
Work = 22 N x 7.50 m x 0.5
Work = 11 N·m
Therefore, the work done by the applied force is 11 N·m.
b) To find the friction force, we need to consider that the net force in the horizontal direction is zero (since the cart is not accelerating horizontally). The horizontal force is the applied force (22 N) multiplied by the cosine of the angle.
Horizontal force = 22 N x cos(60°) = 22 N x 0.5
Horizontal force = 11 N
Since the net horizontal force is zero, the friction force must be equal to the horizontal force but in the opposite direction, i.e., 11 N.
Therefore, the friction force is 11 N.