Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 11.2 m long. His speed at the bottom of the swing is 7.4 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 ✕ 103 N. What is the largest mass that Tarzan can have and still make it safely across the river?
what is mg + mv^2/r? Is that over What m will exceed the given breaking strength?
how would i find mass?
what is the equation that i would use to figure out this answer?
@bobpursley could you help me solve it
mg + mv^2/r = 1000 Newtons
g = 9.81 m/s^2
v = 7.4 m/s
r = 11.2 m
solve for m
To find the largest mass that Tarzan can have and still make it safely across the river, we need to consider the tension in the vine during the swing.
Let's start by considering the forces acting on Tarzan during the swing. At the bottom of the swing, the tension in the vine provides the centripetal force required to keep Tarzan moving in a circular path. The tension is also responsible for supporting Tarzan's weight.
The centripetal force (F_c) is given by the equation:
F_c = (m * v^2) / r
Where:
m is Tarzan's mass (in kg),
v is the speed at the bottom of the swing (in m/s),
r is the radius of the swing (in m).
In this case, the radius of the swing is equal to the length of the vine, so r = 11.2 m. The centripetal force is provided by the tension in the vine.
Therefore, we can write the equation for tension (T):
T = (m * v^2) / r
In order to solve for the largest mass that Tarzan can have, we need to find the maximum tension that the vine can withstand.
Given that the breaking strength of the vine is 1.0 ✕ 10^3 N, we can equate the tension to the breaking strength:
T = 1.0 ✕ 10^3 N
Now we can plug in the given values and solve for the mass (m):
1.0 ✕ 10^3 N = (m * (7.4 m/s)^2) / 11.2 m
Now, let's solve for m by rearranging the equation:
m = (1.0 ✕ 10^3 N * 11.2 m) / (7.4 m/s)^2
m ≈ 208 kg
Therefore, the largest mass that Tarzan can have and still make it safely across the river is approximately 208 kg.