A ball of mass m = 0.75 kg is thrown straight upward with an initial speed of 8.9 m/s. Plot the gravitational potential energy of the block from its launch height, y = 0, to the height y = 5.0 m. Let U = 0 correspond to y = 0. Determine the turning point (maximum height) of this mass.
GPE= m*g*height
looks like a straight line to me.
The key here, and you were not asked to do it, is plot also the kinetic energy on the same graph.
KE=1/2 m v^2=1/2 m (vi^2-2*9.8h)
the sum of GPE and KE should be constant on the graph as in
mgh+1/2 m (vi^2-19.6h)=
mgh+1/2 m*2gh+1/2 mvi^2=
1/2 mvi^2 amazing, a constant.
If a baseball is thrown 30 m/s backwards from a truck moving 50 m/s, how fast will the ball strike the glove of a ground-based catcher
30 m/s - 50 m/s= -20m/s
the backwards represents subtraction. so simply subtract 30 - 50 = -20
To plot the gravitational potential energy of the ball from its launch height to a certain height, we need to determine the potential energy at different heights and then create a graph.
The gravitational potential energy (U) of an object near the surface of the Earth is given by the equation:
U = m * g * h
Where:
m is the mass of the object (0.75 kg in this case)
g is the acceleration due to gravity (approximately 9.8 m/s^2 near the surface of the Earth)
h is the height above the reference point
Since U = 0 corresponds to y = 0, we can calculate the potential energy at various heights above the ground using this equation.
Let's calculate the potential energy at the given height of y = 5.0m:
U = m * g * h
U = 0.75 kg * 9.8 m/s^2 * 5.0 m
U = 36.75 J
Now, we can plot the gravitational potential energy of the ball at different heights. Calculate the potential energy at different heights (0m to 5m) using the same equation and plot the points on a graph with height (y) on the x-axis and potential energy (U) on the y-axis.
To determine the turning point or maximum height, we need to find the height at which the potential energy is maximum. This occurs when the kinetic energy of the ball is zero (at the highest point of the trajectory). At this point, all of the initial kinetic energy of the ball has been converted to gravitational potential energy.
To find the turning point:
1. First, calculate the initial kinetic energy (KE_initial) of the ball when it is thrown upward. The kinetic energy is given by the equation:
KE = (1/2) * m * v^2
Where:
m is the mass of the object (0.75 kg)
v is the initial velocity of the ball (8.9 m/s)
KE_initial = (1/2) * 0.75 kg * (8.9 m/s)^2
KE_initial = 29.77 J
2. At the maximum height, all of this kinetic energy is converted to potential energy:
PE_max = KE_initial
Therefore, the turning point or maximum height is the height at which the potential energy equals the initial kinetic energy: U = 29.77 J.
By plotting the graph and finding the point where the potential energy equals 29.77 J, you can determine the turning point or maximum height of the ball.