A person pushes a 16.5-kg shopping cart at a constant velocity for a distance of 36.6 m on a flat horizontal surface. She pushes in a direction 27.9 ° below the horizontal. A 48.1-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.
M*g = 16.5 * 9.8 = 161.7 N. = Wt. 0f cart.
a. F*Cos27.9-Fk = M*a.
0.884F - 48.1 = M*0 = 0.
0.884F = 48.1.
F = 54.4 N. = Force exerted.
b. Work = F*d = 54.4 * 36.6 = 1992 J.
c. Work = Fk*d = 48.1 * 36.6 = 1760 J.
d. Work=Mg * d = 161.7 * 36.6 = 5918 J.
To find the magnitude of the force that the shopper exerts, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration.
In this case, since the cart is moving at a constant velocity, the net force is equal to zero. Therefore, the force exerted by the shopper must be equal in magnitude but opposite in direction to the frictional force.
(a) The magnitude of the force that the shopper exerts is equal to the magnitude of the frictional force, which is given as 48.1 N.
To determine the work done by different forces, we can use the formula:
Work = Force * Distance * cos(theta)
Where:
- Work is the energy transferred to or from an object
- Force is the magnitude of the force applied
- Distance is the distance moved by the object under the force
- theta is the angle between the force and the direction of motion
(b) For the pushing force, the angle between the force and the direction of motion is given as 27.9° below the horizontal. Therefore, we can calculate the work done by the pushing force as:
Work (pushing force) = Force (shopper) * Distance * cos(theta)
= 48.1 N * 36.6 m * cos(27.9°)
(c) For the frictional force, the angle between the force and the direction of motion is 180° (as it opposes the motion). Therefore, the work done by the frictional force can be calculated as:
Work (frictional force) = - Force (friction) * Distance * cos(180°)
= - 48.1 N * 36.6 m * cos(180°)
(d) The gravitational force can be calculated by multiplying the mass of the cart with the acceleration due to gravity, which is approximately 9.8 m/s^2. Therefore, the gravitational force can be calculated as:
Force (gravity) = Mass * Acceleration due to gravity
= 16.5 kg * 9.8 m/s^2
Since the cart is moving at a constant velocity and there is no change in height, the work done by the gravitational force is zero (as the gravitational force does not do any work on the cart).
So, to summarize:
(a) The magnitude of the force that the shopper exerts is 48.1 N (opposite in direction to the frictional force).
(b) The work done by the pushing force is calculated using the Work formula mentioned above.
(c) The work done by the frictional force is calculated using the Work formula mentioned above.
(d) The work done by the gravitational force is zero.