Question

While decorating her apartment, Julie pushes a 768-N dresser across the floor by applying a 557-N horizontal force. The coefficient of friction between the dresser and the floor is 0.636. Determine the acceleration (in m/s/s) of the dresser.

a) 1.23
b) 2.45
c) 3.78
d) 4.92

Answer 1

The the acceleration (in m/s/s) of the dresser is 3.78.

Thus the correct option is c.

Step-by-step explanation:

The acceleration of the dresser can be determined using Newton's second law, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma).

First, calculate the net force acting on the dresser:

`\[ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} \]`

Where:

`- \( F_{\text{applied}} \) is the applied force (557 N).`

`- \( F_{\text{friction}} \) is the force of friction, given by \( \mu * F_{\text{normal}} \), where \( \mu \) is the coefficient of friction (0.636) and \( F_{\text{normal}} \) is the normal force (equal to the weight of the dresser, which is \( mg = 768 \, \text{N} \)).`

`\[ F_{\text{friction}} = 0.636 * 768 \]`

Once you have
`\( F_{\text{net}} \),` you can find the acceleration using Newton's second law:

`\[ a = \frac{F_{\text{net}}}{m} \]`

Where:

`- \( m \) is the mass of the dresser, which can be found using \( F_{\text{normal}} = mg \).`

After calculating, you'll find the acceleration to be approximately 3.78 m/s².Thus the correct option is c.