A curling stone is moving at a velocity of 8 m/s stops after sliding 5 m across a surface that has 70 N of friction. What is the stone’s mass?
To find the mass of the curling stone, you can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, the force acting on the curling stone is the force of friction. The frictional force (F) can be calculated using the equation: F = coefficient of friction (µ) * normal force (N).
We know that the frictional force is 70 N and the stone stops after sliding 5 m. Therefore, the acceleration of the stone can be calculated using the equation: acceleration (a) = change in velocity (Δv) / time (t).
Since the stone stops, its final velocity (v) is 0 m/s. Thus, the change in velocity (Δv) is equal to the initial velocity (u) of 8 m/s.
Now, let's calculate the acceleration (a). Rearranging the formula: a = Δv / t, we have a = (-8 m/s - 0 m/s) / t.
Since the stone stops after sliding 5 m, we can use the equation: distance (d) = initial velocity (u) * time (t) + (1/2) * acceleration (a) * time squared (t^2).
Plugging in the values, we have 5 m = 8 m/s * t + (1/2) * (-8 m/s / t) * t^2.
Simplifying the equation, we get 0 = 8t - 4t^2.
Rearranging and factoring, we have 4t^2 - 8t = 0.
Taking out common factor 4t, we have 4t(t - 2) = 0.
So, t = 0 or t = 2.
Since t cannot be zero (as the stone is sliding), we have t = 2 seconds.
Now, we can calculate the acceleration (a) using the equation a = (-8 m/s - 0 m/s) / (2 seconds), which gives us a = -4 m/s^2.
Next, let's calculate the normal force (N) using the equation N = m * g, where g is the acceleration due to gravity (approximately 9.8 m/s^2).
So, N = m * 9.8 m/s^2.
Now, we can calculate the frictional force (F = µ * N). We know F = 70 N. Therefore, 70 N = µ * (m * 9.8 m/s^2).
Dividing both sides by 9.8 m/s^2, we have 7.14 = µ * m.
Finally, we can solve for the mass (m) by dividing both sides by µ. Since the coefficient of friction (µ) is not mentioned in the question, we cannot determine the exact mass of the stone without that information.
To summarize:
- The acceleration (a) is -4 m/s^2.
- The normal force (N) can be calculated using N = m * 9.8 m/s^2.
- The frictional force (F) is given as 70 N.
- Using the equation 70 N = µ * (m * 9.8 m/s^2), we can solve for the mass (m) if the coefficient of friction (µ) is provided.
To determine the mass of the curling stone, we need to use the equation that relates force, mass, and acceleration.
First, let's determine the acceleration of the curling stone using the equation of motion:
Final velocity^2 = Initial velocity^2 + 2 * acceleration * distance
Since the stone comes to a stop, the final velocity is 0 m/s. The initial velocity is 8 m/s, and the distance is 5 m. Plugging in these values into the equation:
0^2 = 8^2 + 2 * acceleration * 5
Simplifying the equation:
64 = 10 * acceleration
acceleration = 64 / 10
acceleration = 6.4 m/s^2
Now, let's use Newton's second law of motion:
force = mass * acceleration
The force acting in the opposite direction to the stone's motion is the friction force of 70 N. Plugging in the values:
70 N = mass * 6.4 m/s^2
To isolate the mass, divide both sides of the equation by acceleration:
mass = 70 N / 6.4 m/s^2
Calculating this:
mass = 10.9375 kg
Therefore, the curling stone's mass is approximately 10.94 kg.
work to stop ... 5 m * 70 N = 350 Joules
... this equals the initial K.E.
K.E. = 1/2 m v^2
350 = 1/2 * m * 8^2 ... m is in kg
V^2 = Vo^2 + 2a*d = 0
8^2 + 2a*5 = 0
a = -6.4 m/s^2.
Mg = M*9.8 = Wt. of stone.
M*9.8 - 70 = M*a
9.8M-70 = -6.4M
16.2M = 70
M = 4.3 kg.