Question

Calculate the linear acceleration of the snowball as it rolls down the inclined section of the roof.

Answer 1

To calculate the linear acceleration of the snowball as it rolls down the inclined section of the roof, we use the formula a = g * sin(θ), where g is the acceleration due to gravity and θ is the angle of the slope. Substituting the given values, we find that the linear acceleration is approximately 0.85 m/s^2.

Step-by-step explanation:

To calculate the linear acceleration of the snowball as it rolls down the inclined section of the roof, we need to consider the forces acting on the snowball. The force that causes the snowball to accelerate is the component of the gravitational force parallel to the inclined plane. This force can be calculated using the formula:

a = g * sin(θ)

where a is the linear acceleration, g is the acceleration due to gravity, and θ is the angle of the slope.

In this case, since the angle of the slope is given as 5.00⁰, we substitute the values into the formula to get:

a = 9.8 m/s^2 * sin(5.00⁰)

Calculating this, the linear acceleration of the snowball as it rolls down the inclined section of the roof is approximately 0.85 m/s^2.

Answer 2

To calculate the linear acceleration of a snowball on an inclined plane, use the formula a = g(sin θ - μ_k cos θ), considering gravity, the slope's angle, and the coefficient of kinetic friction. Break down the forces into components parallel and perpendicular to the slope, and apply Newton's second law to find the acceleration.

Step-by-step explanation:

Calculating Linear Acceleration on an Incline

To calculate the linear acceleration of a snowball as it rolls down an inclined plane, we can use Newton's second law and account for the forces acting on the object, such as gravity and friction. The general formula for acceleration on an incline where friction is acting is a = g(sin θ - μ_k cos θ), where a is the acceleration, g is the acceleration due to gravity, θ is the angle of incline, and μ_k is the coefficient of kinetic friction. This equation shows us that the acceleration is independent of the mass of the object. A common approach to solve these problems includes decomposing the weight into components parallel and perpendicular to the slope and applying Newton's second law in the direction of the movement, which incorporates the frictional force.

For instance, if a skier is heading down a 10.0° slope with a coefficient of friction for waxed wood on wet snow, the components of weight are Wx = mg sin(10.0°) and Wy = mg cos(10.0°). The frictional force opposing motion is f_k = μ_k N = μ_k mg cos(10.0°). The net force causing acceleration/downslope motion is given by F_net = Wx - f_k, which can then be used to determine the acceleration using Newton's second law (F = ma).