2.A 3.65 kg mass is hung from a spring with a k constant of 535.0 N/m. How far does the spring stretch?
3.A 35 kg crate slides from rest down a ramp inclined at 29o onto a spring with a force constant of 4.5 x 102 N/m. The spring is compressed a distance of 0.45 m before the crate stops. Determine the total distance the crate slides along the ramp before encountering the spring. Friction is negligible. (Hint: use the LCE not kinematics or dynamics to solve).
4.As new packages are unloaded from the back of a truck, they are slid down a ramp and stopped by a large spring at the bottom of the ramp. A 235 kg package is pushed down the ramp with an initial speed of 1.20 m/s. If the spring at the bottom of the ramp has a spring constant of 220.0 N/m and it compresses 0.450 m when the package lands on it, what is the coefficient of friction along the ramp?
5.A 0.25 kg hockey puck is sliding along a smooth, flat section of ice at 21 m/s when it encounters some snow. After 2.5 s of sliding through the snow, it returns to smooth ice, continuing at a speed of 15 m/s. Neglect friction when the puck is on the smooth ice.
a)What is the change in momentum of the puck?
b)What impulse does the snow exert on the puck?
c)What average frictional force does the snow exert on the puck?
6.A 25 g superball rolls with a velocity of 4.56 m/s [fwd] toward another stationary superball. The balls have a head-on elastic collision. After the collision, the first ball has a velocity of 0.85 m/s [back] and the second ball has a velocity of 7.51 m/s [fwd]. What is the mass of the second ball?
7.An electron (me = 9.11 x 10-31 kg) initially moving 1.25 x 103 m/s [fwd] collides with a proton (mp = 1.67 x 10-27 kg) travelling 2.35 x 102 m/s [back]. The two particles annihilate each other to form a neutron (mn = 1.67 x 10-27 kg). If momentum is conserved in this completely inelastic collision, what is the speed of the neutron produced?
8.A quarterback for the Toronto Argos has a mass of 98 kg and is initially moving backwards at 0.35 m/s when he is tackled by a 112 kg linebacker moving towards him at 3.8 m/s. If the two players stay together throughout the tackle, what will be their final velocity?
9.Two automobiles collide at an intersection. One car of mass 1.45x103 kg is travelling at 65 km/h [S]; the other car of mass 1.65x103 kg is travelling at 48 km/h [E]. If the cars have a completely inelastic collision, what is their velocity just after the collision?
10.A 1.25 kg grenade sits at rest on the ground in an open field when it explodes into 3 pieces. A 0.25 kg piece flies off at 18.5 m/s [N 25o E] and a 0.85 kg piece flies West at 12.4 m/s. What is the velocity of the third piece?
Show us the effort you have made on any of these problems. We will not do your homework for you.
2. To find how far the spring stretches, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. The formula for Hooke's law is F = -kx, where F is the force, k is the spring constant, and x is the displacement.
In this case, the mass is hung from the spring, so the force equals the weight of the mass, which can be calculated as F = mg, where m is the mass and g is the acceleration due to gravity.
So we have the equation mg = -kx.
Rearranging the equation, we get x = -mg/k.
Plugging in the values - mass = 3.65 kg, k = 535.0 N/m, and g = 9.8 m/s^2 (acceleration due to gravity), we can calculate the displacement x.