Two forces are applied to a 0.5 kg hockey puck causing it to accelerate. The first force has a magnitude of 10.0 N and is applied to the puck at an angle of 80 degrees with respect to the x axis. The second force has a magnitude of 3.5 N and is applied to the puck at an angle of 10 degrees with respect to the x axis.
What is the magnitude of the acceleration?
Fr = F1+F2 = 10N[80o] + 3.5N[10o].
X = 10*Cos80 + 3.5*Cos10 = 5.18 N.
Y = 10*sin80 + 3.5*sin10 = 10.5 N.
Fr = = sqrt(x^2+y^2) = (5.18^2+10.5^2) = 11.7 N, = Resultant force.
Fr = M*a = 11.7, a = 11.7/M = 11.7/0.5 = 22.14 m/s^2.
To find the magnitude of the acceleration, we can use Newton's second law of motion, which states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass.
First, let's find the x and y components of each force:
For the first force with a magnitude of 10.0 N and an angle of 80 degrees:
Fx1 = 10.0 N * cos(80 degrees)
Fy1 = 10.0 N * sin(80 degrees)
For the second force with a magnitude of 3.5 N and an angle of 10 degrees:
Fx2 = 3.5 N * cos(10 degrees)
Fy2 = 3.5 N * sin(10 degrees)
The net force in the x-direction (Fx_net) can be found by summing the x-components of the forces:
Fx_net = Fx1 + Fx2
The net force in the y-direction (Fy_net) can be found by summing the y-components of the forces:
Fy_net = Fy1 + Fy2
Next, we can calculate the net force (F_net) using the Pythagorean theorem:
F_net = sqrt((Fx_net)^2 + (Fy_net)^2)
Finally, we can determine the magnitude of the acceleration (a) using Newton's second law:
a = F_net / mass
Plugging in the values:
Mass (m) = 0.5 kg
Fx_net = Fx1 + Fx2
Fy_net = Fy1 + Fy2
Calculate F_net = sqrt((Fx_net)^2 + (Fy_net)^2)
Finally, calculate a = F_net / mass.
By following these steps, you can find the magnitude of the acceleration.