Physics, 26.07.2019 15:30 aupein

A10 kg runaway grocery cart runs into a spring with spring constant 250 n/m and compresses it by 60 cm. what was the speed of the cart just before it hit the spring?

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Answer from: 99keevintaylor012

The initial speed of the cart is 3 m/s.

What is the velocity?

The velocity of an object is the rate of change of its position with respect to a given time interval.

Given that the mass m of the cart is 10 kg and the spring constant is 250 N/m. The compressed length of the spring is 60 cm.

The initial kinetic energy of the cart is given below.

$KE = \dfrac {1}{2}mv^2$

Where v is the initial velocity of the cart.

When the cart hits the spring, it is compressed by the cart. When the cart stops, due to the maximum compression, the kinetic energy of the cart will be zero. Hence its kinetic energy will be converted into elastic potential energy of the spring. This is given as,

$U = \dfrac {1}{2} kx^2$

Where k is the spring constant and x is the compressed length of the spring.

$U = \dfrac {1}{2} \times 250 \times 0.60^2$

$U = 45 \;\rm J$

This elastic potential energy of the spring will be equal to the initial kinetic energy of the cart.

$45 = \dfrac {1}{2} \times 10 \times v^2$

90 = 10 v^2

v^2 = 9

$v = 3 \;\rm m/s$

Hence we can conclude that the initial speed of the cart is 3 m/s.

To know more about the velocity, follow the link given below.

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Answer from: spazzinchicago

The initial kinetic energy of the cart is
$K= \frac{1}{2} mv^2$ (1)
where m is the mass of the cart and v its initial velocity.

Then, the cart hits the spring compressing it. The maximum compression occurs when the cart stops, and at that point the kinetic energy of the cart is zero, so all its initial kinetic energy has been converted into elastic potential energy of the spring:
$U= \frac{1}{2}kx^2$
where k is the spring constant and x is the spring compression.

For energy conservation, K=U. We can calculate U first: the compression of the spring is x=60 cm=0.60 m, while the spring constant is k=250 N/m, so
$U= \frac{1}{2}kx^2= \frac{1}{2}(250 N/m)(0.60 m)^2=45 J$

So, the initial kinetic energy of the cart is also 45 J, and from (1) we can find the value of the initial velocity:
$v= \sqrt{ \frac{2K}{m} }= \sqrt{ \frac{2 \cdot 45 J}{10 kg} } =3 m/s$

Answer from: Quest

number of electrons for neutral cl

Answer from: Quest

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.