A hockey stick applies a constant force over a distance of 0.127 m to an initially stationary puck, of mass 152 g. The puck moves with a speed of 51.0 m/s. With what force did the hockey stick strike the puck?
To find the force with which the hockey stick struck the puck, we can use the principle of work and energy.
The work done on an object is given by the equation:
Work = Force * Distance * cos(theta)
Where:
- Work is the amount of energy transferred to or from an object
- Force is the applied force on the object
- Distance is the distance over which the force is applied
- theta is the angle between the force and the direction of motion
In this case, the distance over which the force was applied is given as 0.127 m. The angle between the force and the direction of motion is not given, but we will assume it to be 0° (since the puck is initially stationary, we can assume that the force is applied in the direction of motion).
The work done on the puck is equal to its change in kinetic energy:
Work = Change in kinetic energy
The change in kinetic energy can be calculated as:
Change in kinetic energy = (final kinetic energy) - (initial kinetic energy)
The final kinetic energy of the puck is given as:
Final kinetic energy = (1/2) * mass * (final velocity)^2
The initial kinetic energy of the puck is assumed to be zero since it is initially stationary.
Let's substitute the given values into the equations:
Final kinetic energy = (1/2) * 0.152 kg * (51.0 m/s)^2
Change in kinetic energy = (1/2) * 0.152 kg * (51.0 m/s)^2 - 0
Now, recall that the work done on the puck is equal to its change in kinetic energy:
Work = Change in kinetic energy
So,
Force * Distance * cos(theta) = (1/2) * 0.152 kg * (51.0 m/s)^2
Now, solving for force:
Force = [(1/2) * 0.152 kg * (51.0 m/s)^2] / (0.127 m * cos(0°))
Calculating this expression will give you the force with which the hockey stick struck the puck.
To find the force with which the hockey stick struck the puck, we can use Newton's second law of motion, which states that force (F) is equal to the mass (m) of an object multiplied by its acceleration (a). In this case, the puck moves with a certain speed, which we can use to find its acceleration.
First, let's convert the mass of the puck from grams to kilograms. Since there are 1000 grams in a kilogram, the mass of the puck is 152 g / 1000 = 0.152 kg.
Next, we need to find the acceleration of the puck. We can use the equation of motion, v^2 = u^2 + 2as, where v is the final velocity, u is the initial velocity (which is zero since the puck is initially stationary), a is the acceleration, and s is the distance traveled.
Rearranging the equation, we get a = (v^2 - u^2) / (2s). Plugging in the values, we have a = (51.0 m/s)^2 / (2 × 0.127 m) = 130.748 m/s^2.
Now we can calculate the force using Newton's second law of motion. F = m × a = 0.152 kg × 130.748 m/s^2 = 19.894 N.
Therefore, the hockey stick struck the puck with a force of approximately 19.894 Newtons.
Hmmm.
v = at
51 = at
s = 1/2 at^2
2s = at^2
.254 = at^2 = at*t
.254 = 51*t
t = .00498
51 = .00498a
a = 10240.963
F = ma = .152 a = 1556.6