Question

. Emily pushes a 38.8 kg grocery cart of groceries by exerting a 76.0 N force on the handle inclined at 40.0 degrees below the horizontal. What are:
a. The horizontal and vertical components of Emily’s force






b. The acceleration of the cart?

Answer 1

Answer:

a) $F_{x} = 58.2 N$

$F_{y} = 48.9 N$

b) a = 1.5 m/s²

Explanation:

a) The horizontal and vertical components of Emily's force can be found knowing the angle and the exerted force.

Since the handle is inclined at 40.0° below the horizontal we have:

$F_{x} = |F|*cos(\theta) = 76.0 N*cos(40) = 58.2 N$

$F_{y} = |F|*sin(\theta) = 76.0 N*sin(40) = 48.9 N$

b) The acceleration of the car can be calculated as follows:

$F_{x} = ma$        

We used the horizontal component of the force because the cart is moving in that direction.

$a = \frac{F_{x}}{m} = \frac{58.2 N}{38.8 kg} = 1.5 m/s^{2}$

Hence, the acceleration of the car is 1.5 m/s².    

I hope it helps you!