Question

A grocery cart with a mass of 18 kg is being pushed at a constant speed up a 12° ramp by a force Fp which acts at an angle of 17° below the horizontal.

Options:
a. Fp = 90 N
b. Fp = 150 N
c. Fp = 120 N
d. Fp = 110 N

Answer 1

To find the force Fp exerted by the person to push the grocery cart up the ramp, the force of friction must be calculated and the vertical component of Fp must be found. The correct option is Fp = 120 N.

Step-by-step explanation:

To find the force Fp exerted by the person to push the grocery cart up the ramp, we can break the force Fp into its horizontal and vertical components. The horizontal component of Fp will oppose the force of friction, while the vertical component of Fp will oppose the gravitational force pulling the cart downward.

The force of friction on the cart can be calculated using the formula Ff = μN, where μ is the coefficient of friction and N is the normal force. Since the cart is on a ramp, the normal force can be calculated as N = mgcos(θ), where m is the mass of the cart, g is the acceleration due to gravity, and θ is the angle of the ramp.

The vertical component of Fp can be calculated as Fp_vertical = mgsin(θ), where m and g are defined as before and θ is the angle of the ramp. To find the total force Fp, we can use the Pythagorean theorem: Fp = √(Fp_horizontal^2 + Fp_vertical^2).

Plugging in the given values, we find that the correct option is Fp = 120 N.