dynamics
A curling stone has a mass of 20kg. a curler pushed the stone across the ice to launch it down the rink.
a)if the curler starts to move the stone by pushing it with 15N, what is the stones initial acceleration?
b)once moving, how much force is required to keep the stone moving at a uniform velocity?
a) To find the initial acceleration, we can use Newton's second law of motion, which states that Force = mass x acceleration, or F = m*a. We can rearrange the equation to find the acceleration: a = F/m.
Given the force (F) is 15N, and the mass (m) of the curling stone is 20kg, we can calculate the acceleration:
a = F / m
a = 15N / 20kg
a = 0.75 m/s²
So the initial acceleration of the curling stone is 0.75 m/s².
b) Once the stone is moving at a uniform velocity, it means that there is no acceleration, so the net force acting on it is zero. Therefore, to keep the stone moving at a uniform velocity, the force required must be equal to the frictional force acting on the stone in the opposite direction. In the case of curling, the frictional force is usually very small because the ice surface is very slippery. So, very little force will be required to maintain its uniform velocity.
a) To find the initial acceleration of the stone, we 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.
Given:
Mass of the stone (m) = 20 kg
Force applied (F) = 15 N
Using the formula F = ma, we can rearrange it to find the acceleration (a):
a = F / m
Substituting the given values, we get:
a = 15 N / 20 kg
a = 0.75 m/s²
Therefore, the stone's initial acceleration is 0.75 m/s².
b) Once the stone is moving at a uniform velocity, it means that the net force acting on it is zero. In other words, the force required to keep the stone moving at a uniform velocity is equal and opposite to the force of friction acting on it.
To find the force of friction, we can use the equation:
Frictional force (Ff) = coefficient of friction (μ) * Normal force (Fn)
Since the stone is on a horizontal surface, the normal force is equal to the weight of the stone, which is given by:
Weight (W) = mass (m) * acceleration due to gravity (g)
Given:
Mass of the stone (m) = 20 kg
Acceleration due to gravity (g) ≈ 9.8 m/s²
Coefficient of friction (μ) = assume an appropriate value
Substituting these values, we can find the normal force:
Fn = 20 kg * 9.8 m/s²
Fn = 196 N
Assuming a coefficient of friction, let's say μ = 0.1:
Ff = 0.1 * 196 N
Ff = 19.6 N
Therefore, the force required to keep the stone moving at a uniform velocity is approximately 19.6 N.
To find the answers to these questions, we need to apply Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force applied to it and inversely proportional to its mass.
a) To calculate the stone's initial acceleration, we can use the formula:
Acceleration = Net force / Mass
Given that the curler pushes the stone with a force of 15N and the stone has a mass of 20kg, we substitute these values into the formula:
Acceleration = 15N / 20kg = 0.75 m/s²
Therefore, the stone's initial acceleration is 0.75 m/s².
b) Once the stone is moving at a uniform velocity, it means that its acceleration is zero. According to Newton's second law, if the acceleration is zero, the net force acting on the stone must also be zero.
Therefore, to keep the stone moving at a uniform velocity, no force is required. Once it is moving, it will continue moving in a straight line at a constant speed (uniform velocity) unless acted upon by another force, such as friction.