A force of 8,480 N is applied to a cart to accelerate it at a rate of 26.5 m/s2. What is the mass of the cart?

Physics

2 answers:

Anni [7]3 years ago

8 0

F=ma
8480=26.5m
m=8480/26.5
m=320
The mass of the cart is 320kg.

velikii [3]3 years ago

4 0

For the given question, the mass of the cart is 320 Kg.

Answer: Option B

<u>Explanation:</u>

According to Newton’s second law, the rate of change in momentum exerted by an object is directly proportional to the unbalanced force exerted on the object. So

$\text {Unbalanced Force } F=\frac{d(\text {momentum})}{d t}$

As momentum of an object is derived from the product of mass and velocity of the object. Thus,

$\text {Momentum}=m \times v$

So,

$\text {Unbalanced Force } F=\frac{d(m \times v)}{d t}$

As mass of an object tend to be same irrespective of time and velocity can vary with time, we obtain,

$\text {Unbalanced Force } F=m \times \frac{d v}{d t}=m \times \text { accelearation }$

As it is known that rate of change in velocity is equal to the acceleration exerted by the object. Thus, Newton’s second law can also be stated as that the external unbalanced force exerted on the object will be equal to the mass of the object and the acceleration exerted by the object. So in the present case, as we known the force and acceleration, the mass of the object will be determined by the formula F = ma.

$F=m \times \text {acceleration}$

Therefore,

$\text {Mass}=\frac{\text { Force }}{\text { Acceleration }}=\frac{8480}{26.5}=320 \mathrm{kg}$

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