Answer:
1.15 m/s
Explanation:
Part of the question is missing. Found the missing part on google:
"1. A hanging mass of 1500 grams compresses a spring 2.0 cm. Find the spring constant in N/m."
Solution:
First of all, we need to find the spring constant. We can use Hooke's law:
[tex]F=kx[/tex]
where
[tex]F=mg=(1.5 kg)(9.8 m/s^2)=14.7 N[/tex] is the force applied to the spring (the weight of the hanging mass)
x = 2.0 cm = 0.02 m is the compression of the spring
Solving for k, we find the spring constant:
[tex]k=\frac{F}{x}=\frac{14.7}{0.02}=735 N/m[/tex]
In the second part of the problem, the spring is compressed by
x = 3.0 cm = 0.03 m
So the elastic potential energy of the spring is
[tex]U=\frac{1}{2}kx^2=\frac{1}{2}(735)(0.03)^2=0.33 J[/tex]
This energy is entirely converted into kinetic energy of the cart, which is:
[tex]U=K=\frac{1}{2}mv^2[/tex]
where
m = 500 g = 0.5 kg is the mass of the cart
v is its speed
Solving for v,
[tex]v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(0.33)}{0.5}}=1.15 m/s[/tex]
